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These moves were selected by Stockfish running on a decent 2-core CPU at 30 minutes per move. While Stockfish is a fine engine, computers aren't great at the end game, so I expect that there could be some improvements.

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Ke6 2.Ke2 Kd5 3.Kd3 Ne7 4.a4 Nc8 5.Ne3+ Kc6 6.Nf5 g6 7.Nd4+ Kc7 8.Nb3 h4 9.Nc5 Kb6 10.Nd7+ Kc6 11.Ne5+ Kd5 12.Nxf7 Nd6 13.Nxd6 Ke6 14.Ne4 *

...and it's lights-out for Black.

What we see here for the first 7 half-moves are both players centralizing their Kings and preparing for a skirmish on the Queenside. Black's 4th move looks to be a clunker though it is still about bringing the Knight to the Queenside. What's happening here is that White is taking the slack out of the Queenside and limiting Black's response. This makes additional calculation easier.

White punishes 4...Nc8 by a series of Knight moves that harass the Black King, which must stay near the Queenside. A fork develops and Black loses material without compensation on the Kingside. Black can honorably resign after White's 11th move, IMO.

After 13.Nxd6 there are no good moves and Stockfish goes wonky. It hardly matters - Black is done.

The strategies in the position are:

1. Black will try to equalize on the Queenside
2. White will be willing to surrender two pawns for one pawn on the Queenside, as long as the Black King is misplaced (decoyed!) to the rim. White's King can then run amok on the Kingside.

To answer the OP's question, yes this is winnable. First, it looks to me like White can win with proper play. Second, unless you're playing at a very high level, nearly every position is winnable - you just have to capitalize on the opponent's mistakes. Chess is a game about outwitting your opponent, not making perfect moves.

These moves were selected by Stockfish running on a decent 2-core CPU at 30 minutes per move. While Stockfish is a fine engine, computers aren't great at the end game, so I expect that there could be some improvements.

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Ke6 2.Ke2 Kd5 3.Kd3 Ne7 4.a4 Nc8 5.Ne3+ Kc6 6.Nf5 g6 7.Nd4+ Kc7 8.Nb3 h4 9.Nc5 Kb6 10.Nd7+ Kc6 11.Ne5+ Kd5 12.Nxf7 Nd6 13.Nxd6 Ke6 14.Ne4 *

...and it's lights-out for Black.

What we see here for the first 7 half-moves are both players centralizing their Kings and preparing for a skirmish on the Queenside. Black's 4th move looks to be a clunker though it is still about bringing the Knight to the Queenside. What's happening here is that White is taking the slack out of the Queenside and limiting Black's response. This makes additional calculation easier.

White punishes 4...Nc8 by a series of Knight moves that harass the Black King, which must stay near the Queenside. A fork develops and Black loses material without compensation on the Kingside. Black can honorably resign after White's 11th move, IMO.

After 13.Nxd6 there are no good moves and Stockfish goes wonky. It hardly matters - Black is done.

The strategies in the position are:

1. Black will try to equalize on the Queenside
2. White will be willing to surrender two pawns for one pawn on the Queenside, as long as the Black King is misplaced (decoyed!) to the rim. White's King can then run amok on the Kingside.

To answer the OP's question, yes this is winnable. First, it looks to me like White can win with proper play. Second, unless you're playing at a very high level, nearly every position is winnable - you just have to capitalize on the opponent's mistakes. Chess is a game about outwitting your opponent, not making perfect moves.

Final edit - I don't see a variation where Black can force a draw. White's extra pawn forces Black to make decisions that are fatal in the long term.

These moves were selected by Stockfish running on a decent 2-core CPU at 30 minutes per move. While Stockfish is a fine engine, computers aren't great at the end game, so I expect that there could be some improvements.

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Ke6 2.Ke2 Kd5 3.Kd3 Ne7 4.a4 Nc8 5.Ne3+ Kc6 6.Nf5 g6 7.Nd4+ Kc7 8.Nb3 h4 9.Nc5 Kb6 10.Nd7+ Kc6 11.Ne5+ Kd5 12.Nxf7 Nd6 13.Nxd6 Ke6 14.Ne4 *

...and it's lights-out for Black.

What we see here for the first 7 half-moves are both players centralizing their Kings and preparing for a skirmish on the Queenside. Black's 4th move looks to be a clunker though it is still about bringing the Knight to the Queenside.

White punishes 4...Nc8 by a series of Knight moves that harass the Black King, which must stay near the Queenside. A fork develops and Black loses material without compensation on the Kingside. Black can honorably resign after White's 11th move, IMO.

After 13.Nxd6 there are no good moves and Stockfish goes wonky. It hardly matters - Black is done.

The strategies in the position are:

1. Black will try to equalize on the Queenside
2. White will be willing to surrender two pawns for one pawn on the Queenside, as long as the Black King is misplaced (decoyed!) to the rim. White's King can then run amok on the Kingside.

To answer the OP's question, yes this is winnable. First, it looks to me like White can win with proper play. Second, unless you're playing at a very high level, nearly every position is winnable - you just have to capitalize on the opponent's mistakes. Chess is a game about outwitting your opponent, not making perfect moves.

These moves were selected by Stockfish running on a decent 2-core CPU at 30 minutes per move. While Stockfish is a fine engine, computers aren't great at the end game, so I expect that there could be some improvements.

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Ke6 2.Ke2 Kd5 3.Kd3 Ne7 4.a4 Nc8 5.Ne3+ Kc6 6.Nf5 g6 7.Nd4+ Kc7 8.Nb3 h4 9.Nc5 Kb6 10.Nd7+ Kc6 11.Ne5+ Kd5 12.Nxf7 Nd6 13.Nxd6 Ke6 14.Ne4 *

...and it's lights-out for Black.

What we see here for the first 7 half-moves are both players centralizing their Kings and preparing for a skirmish on the Queenside. Black's 4th move looks to be a clunker though it is still about bringing the Knight to the Queenside. What's happening here is that White is taking the slack out of the Queenside and limiting Black's response. This makes additional calculation easier.

White punishes 4...Nc8 by a series of Knight moves that harass the Black King, which must stay near the Queenside. A fork develops and Black loses material without compensation on the Kingside. Black can honorably resign after White's 11th move, IMO.

After 13.Nxd6 there are no good moves and Stockfish goes wonky. It hardly matters - Black is done.

The strategies in the position are:

1. Black will try to equalize on the Queenside
2. White will be willing to surrender two pawns for one pawn on the Queenside, as long as the Black King is misplaced (decoyed!) to the rim. White's King can then run amok on the Kingside.

To answer the OP's question, yes this is winnable. First, it looks to me like White can win with proper play. Second, unless you're playing at a very high level, nearly every position is winnable - you just have to capitalize on the opponent's mistakes. Chess is a game about outwitting your opponent, not making perfect moves.

I entered the position into Stockfish and let it grind from anywhere from 1,000 seconds to 8 hours for each move.

White wins by forcing Black's Kind to defend the Queenside, and then shifting his attack to the Kingside.

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Ke6 2.Ke2 Kd5 3.Kd3 Ne7 4.a4 Nc8 5.Ne3+ Kc6 6.Nf5 g6 7.Nd4+ Kc7 8.Nb3 h4 9.Nc5 Kb6 10.Nd7+ Kc6 11.Ne5+ Kd5 12.Nxf7 Nd6 13.Nxd6 Ke6 14.Ne4 *

...and it's lights-out for Black. This was run on a decent 2-core CPU at 30 minutes per move.

What we see here is White pressing his advantage on the Queenside. To prepare for this, he centralizes his King. Don't be fooled - the purpose of moving the King to the center isn't to force one of the Queenside pawns through - it is to make Black commit his King. Then White will surrender his extra pawn to the Black King so his King can run amok on the Kingside.

To answer the OP's question, yes this is winnable. First, it looks to me like White can win with proper play. Second, unless you're playing at a very high level, nearly every position is winnable - you just have to capitalize on the opponent's mistakes. Chess is a game about outwitting your opponent, not making perfect moves.

Anyway, back to the variation above, the move that pokes me in the eye is 4... Nc8

These moves were selected by Stockfish running on a decent 2-core CPU at 30 minutes per move. While Stockfish is a fine engine, computers aren't great at the end game, so I expect that there could be some improvements.

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Ke6 2.Ke2 Kd5 3.Kd3 Ne7 4.a4 Nc8 5.Ne3+ Kc6 6.Nf5 g6 7.Nd4+ Kc7 8.Nb3 h4 9.Nc5 Kb6 10.Nd7+ Kc6 11.Ne5+ Kd5 12.Nxf7 Nd6 13.Nxd6 Ke6 14.Ne4 *

...and it's lights-out for Black.

What we see here for the first 7 half-moves are both players centralizing their Kings and preparing for a skirmish on the Queenside. Black's 4th move looks to be a clunker though it is still about bringing the Knight to the Queenside. 

White punishes 4...Nc8 by a series of Knight moves that harass the Black King, which must stay near the Queenside. A fork develops and Black loses material without compensation on the Kingside. Black can honorably resign after White's 11th move, IMO.

After 13.Nxd6 there are no good moves and Stockfish goes wonky. It hardly matters - Black is done.

The strategies in the position are:

1. Black will try to equalize on the Queenside
2. White will be willing to surrender two pawns for one pawn on the Queenside, as long as the Black King is misplaced (decoyed!) to the rim. White's King can then run amok on the Kingside.

To answer the OP's question, yes this is winnable. First, it looks to me like White can win with proper play. Second, unless you're playing at a very high level, nearly every position is winnable - you just have to capitalize on the opponent's mistakes. Chess is a game about outwitting your opponent, not making perfect moves.